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9.6/ TRIGONOMETRIC FORMULAE
<br /> c
<br /> b'�89 •03' fi "�' ` a a a
<br /> Right Tdagile Oblique Triangles
<br /> q - 3� /Z6� l•;•. Solution of Right'Triangles
<br /> e. '3 7� a 7 / /S3 For Angle A. stx:�o ooe— a ,tan b ,cot-T a,sec=-b, cosec =
<br /> a
<br /> (uvea Requlte4 a r—
<br /> A, N;d isa d = b= cot B,c =vraF2 +
<br /> = a_1 I
<br /> aio -41*A—Q=cosB,b=%/ c+a 02
<br /> f ------"�� 11,a B, Ord $®90°—A,b = a cotA,c= sin A.
<br /> A,b ,^ a B=90°—A,a = b tan A,c= \ f
<br /> q .:
<br /> !
<br /> B B,- , b:. =90°—A,
<br /> Y La o sin A,b= o cos A,
<br /> �
<br /> 1" }. Solution of Oblique Triangles
<br /> 4 0 3 r 9 e AtiB,a b, o; C b=r nR B, a= 180°—(A+B),c =a sin C
<br /> 17 L �,,,....►" y r, •/ sin A
<br /> ._.,,. a l* 1 A b b sin A , a ein a
<br /> a y , �7__ 9 7, f � 71 m , <+s B,q a ein B= a ,C'= 180 -(�-I-B),c =
<br /> -- — � sin A, 2
<br /> 3 / 7.+ os G 7 4 _ 9 L,j 0. b, C d, B,o A+B=180°—C,tan j(A—B)= a—b) +bA -
<br /> �7.6lr/ �,9 1 asinC 1'c'
<br /> 3 v/ ; 3 Z //,z7 /I•e0 sin A
<br /> /`f� /,ass f, 8 _ a'<b, °x a C s=a+2+c,sinjA=l e .b c
<br /> A/ ° l > `/ /$,�(., �` /� ainB=tel`. ao ,C=180°---(A+B)
<br /> /,9 9,00 a+b+
<br /> a, 6, .e. Arta 8= 2 , area = "s(8—a .a—
<br /> 6+11 A; b, c Areiv area b c s2 A �3 , o
<br /> q
<br /> sin B sin a
<br /> 3 i 1 .2 ,��► - '-A,B,C,a A4 : area = f
<br /> 3 y O y. 2sin A
<br /> REDUCTION TO HORIZONTAL
<br /> Horizontal distance—SIboe distance multiplied by the
<br /> t
<br /> /•94 a cosineoftheverticalan¢le.Thus:slopedistance=319.4&
<br /> aN * Vert. angle=60 19: From Table,Page IX.cos 6°ION=
<br /> �---- uSK aorizontal distance=81$.4X.9969=81&O9 ft
<br /> Stogy ASK
<br /> distance also=;Slope distance min l
<br /> distance times W cosine of vertical anope
<br /> 9 ` S S'Q s•1 S qe angle). Wsthe
<br /> y� y / /G.Gy fame figures as in the preceding example,thelollow.
<br /> 8 /D•:�'! Horizontal distanob ing result is obtained.Cositfe 6°101=.88b9.1—.8969=.004L
<br /> 818.4X.00g1=1.91.919.y-1.81=818 08 ft
<br /> / + When the'rise is known,the horizolntal distance
<br /> p 9 �',"f l � / aaoe less thi sure of the rise divided'liq twice is approximately:—the elope dish ftthe slope distance. Thus:rise=14 ,
<br /> slope diatanoe=802 8 ft horizontal distanee=802.6— 4 X 14 ffi90Z".82=802.28 it
<br /> 2X802.6
<br /> IN V.4.A. �.
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